### Math 102 - Calculus I with Economics Applications Reading Assignments - October 2003

Be sure to check back, because this may change during the semester.

I'll use Maple syntax for mathematical notation on this page. All numbers indicate sections from Calculus from Graphical, Numerical, and Symbolic Points of View, Second Edition by Ostebee/Zorn.

### For Wednesday October 1

The Big Picture before Exam 1. No Reading Assignment for today.

### For Friday October 3

Section 2.4 Using Derivative and Antiderivative Formulas

To read : All. Be sure to understand the definition of an antiderivative and Theorems 8, 9, and 10.

1. Explain in your own words what an antiderivative of a function g(x) is.
2. How many antiderivatives does f(x)=3x2 have? Why?

### For Monday October 6

Section 2.6 Derivatives of Exponential and Logarithmic Functions; Modeling Growth

To read : All. Be sure to understand Theorem 12 and the section "Proof by picture" that follows.

1. What is the 82nd derivative of f(x)=ex?
2. Do exponential functions model compound interest well? Explain.

### For Wednesday October 8

Section 2.6 Derivatives of Exponential and Logarithmic Functions: Modeling Growth

### For Friday October 10

Section 2.7 Derivatives of Trignometric Functions: Modeling Oscillation

To read : All. Be sure to understand the section "Differentiating the sine: an analytic proof".

1. What is limh->0 ( cos(h) - 1) / h?
2. What is limh->0 sin(h) / h?
3. Why do we care about the limits in the first two questions?

### For Monday October 13

Fall Break. Surprisingly, no Reading Assignment.

### For Wednesday October 15

Section 3.1 Algebraic Combinations: The Product and Quotient Rules

To read : All. Be sure to understand Examples 3, 4 and 5.

Reading Questions : Explain what is wrong with the following calculations and fix them.
1. f(x)=x2 sin(x).   f'(x)=2x cos(x)
2. g(x)=sin(x) / (x2 + 1).   g'(x) = cos(x) / (2x)

### For Friday October 17

Section 3.2 Composition and the Chain Rule

To read : Through Example 12. We'll consider evidence for why the Chain Rule is true during class.

Reading Questions : Explain what is wrong with the following calculations and fix them.
1. f(x)= sin(x2).   f'(x)=cos(2x)
2. g(x)=( sin(x) )3.   g'(x)=3( cos(x) )2

### For Monday October 20

Section 3.2 Composition and the Chain Rule

### For Wednesday October 22

More fun with differentiation. Review Sections 3.1 and 3.2, but no Reading Assignment.

### For Friday October 24

Differentiation Exam today. No Reading Assignment.

### For Monday October 27

Section 4.3 Optimization

1. At which x-values can a continuous function f(x) achieve its maximum or minimum value on a closed interval [a,b]?
2. What is the difference between an objective function and a constraint equation?

### For Wednesday October 29

Section 4.3 Optimization